I spoke with the Developers about this issue. Unfortunately there doesn't seem to be an immediate solution:

Mosaic runs into the same flashplayer memory issues that
other apps using SWFLoader experience. Mosaic 9.0.1 will include some memory
optimization to help reduce the problem... [Engineering is] working ... to isolate the issues and get a fix.

The original problem was with the Mosaic 9.0 product, and has been fixed since. If you are seeing something similar with the current release (9.5.0.1), then I suspect its another cause (although the symptoms may be similar).